On the emergence of an accidental narrative.

Good writers of fiction will sometimes refer to being surprised at the actions their own characters take. After all, once a story takes a life of its own, in the way that good stories so often do, why should even the author be able to foresee everything that happens?

A similar effect is seen in tabletop gaming, where a good dungeon master (DM--- more correctly, game master) will present a carefully planned adventure to her players only to find that they fixate on details that the DM had thought to be inconsequential. Out of that interaction, a new narrative is drawn from the fibers laid down by the DM. Background material moves to the foreground as the story finds its own vibrancy at the hands of the players and the DM.

Up until recently, I had thought these kinds of emergent narratives to be the province of fiction. On Wednesday, however, I had the pleasure of attending a talk by Ben Schumacher on his experiment with teaching quantum mechanics to undergraduates from a quantum information perspective. In his talk, Dr. Schumacher described how the book that he and Dr. Michael Westmoreland wrote, Quantum Processes Systems, and Information (note: associate link), had a hidden narrative that emerged as they proceeded through the writing process. So as to not spoil the story, I'll refer interested readers to Schumacher's talk for details on the form that this narrative takes.

For my part, I have found that in writing this blog, I tend to write each post relatively independently, with little thought of how they fit together into some cohesive whole. Even the name, cgranade::streams, belies some of this approach. It seems plausible, then, that a narrative could emerge not from careful planning but through recognizing the common concerns which motivate me to write on disparate topics.

That said, I was still surprised to find that when responding to a comment by Sarah Kavassalis on one of my recent posts, a small narrative had started to emerge. In three of my last four posts, I have either alluded to or directly dealt with problems that children face in society, pointing out that they are told that their life experiences are less than real, that the authority figures that abuse them can be defended and even celebrated, and that their nascent sexuality is disrespected and disregarded. In all three of these cases, we see a common strand: children are not always seen as being fully human, and the effects of that are as real and destructive as for any group tarnished as being less than human. Their rights are trounced upon, just as with any marginalized group, illustrating the peril in this disregard.

In this way, a narrative about the disrespect of children by society at large serves as a poignant case study of why recognizing the humanity of those around us is so important. Whether the victims of our disregard by marked by sexual orientation, race, religion or nationality, the end effects share much in common.

I don't know if I'll carry this emergent narrative any farther, or if it has served its useful purpose here. Others write on the modern plights of children better than I do, so that my contribution is to entirely to tie it to other threads of thought. This mission, which I have accidentally worked at, is one of many worthwhile missions. If I have more to say on the topic, then, I will say it and will otherwise be content to hunt for other emergent narratives.

On ideas.

Yes, my blog posting has been slow as of late. Blame working on funding proposals, a lack of good sleep or the phase of the moon if you like. The real problem, though, has been one far more mundane and frustrating: a lack of good ideas.

Ideas are the currency of my career, really, along with hard work and technical skills. Some ideas can be turned into research directions, others into specific solutions to technical problems, and still others become blog posts. Research is, after all, a creative enterprise. What to do, then, when ideas run dry?

The short answer is that I don't think that ideas ever do run dry. We are surrounded by a whole ether of ideas, after all. The trick is finding those ideas which solve your problem, ideas which motivate you, ideas which others may find interesting. It is less, then, that I am short on ideas so much as I am short on ideas that are applicable to the tasks in front of me, including blogging.

Or is it that I am lacking the discipline and energy to refine those ideas into proper posts? After all, writing (like research) doesn't stop with ideas, as Gaiman so gracefully puts it in an essay on writing:

The Ideas aren't the hard bit. They're a small component of the whole. Creating believable people who do more or less what you tell them to is much harder. And hardest by far is the process of simply sitting down and putting one word after another to construct whatever it is you're trying to build: making it interesting, making it new.
[Source: "Where Do You Get Your Ideas," an e-book extra to the Kindle edition of Anansi Boys.]

If there's one thing that life on the Internet teaches, it's that any idea is interesting when placed in the right context and explored with passion. For instance, it seems that much of science fiction works by exploring perhaps mundane ideas in fresh contexts and thus making them new, as Gaiman puts it. Snow Crash doesn't thrive because (to pick a small example out of many from that book) Neal Stephenson invented the idea of a gated community, so much as because he placed it in the context of extreme corporatism and factionalism and thus makes the idea new again in a particularly terrifying way. Manifold: Time isn't a wonderful read because Stephen Baxter invented the idea of the end of the world, but because he puts it in the context of a physically manifest observable and explores the consequences.

Certainly, authors such as Sky McKinnon write based on wonderful ideas, but I think that they have something else to teach us as well: that successful writing is the synthesis of ideas and a dogged enthusiasm for exploring ideas. In that way, writing, be it for a blog or a book, isn't so different from research, even if the tools for exploring the consequences of an idea are very different.

All this leaves me, however, with nary an excuse for my protracted blog silence. Ideas aren't my problem, after all. Oh, well. Maybe I should write a post about how ideas aren't my problem?

Looking back at what is.

Over the past few weeks, I've tried to tunnel through the potential barriers to actual science blogging, with mixed success. One of my bigger oversights thus far has been to omit any sort of a "big picture" from my posts, leaving them as little islands in a vast sea of scientific ideas. Today, I'd like to correct that.

My most immediate goal in science blogging has been to explain how physical states function in the beautiful formalism of quantum mechanics. The language of quantum mechanics, however, is one of probabilities, of complex numbers and of linear algebra. Arguably the most fundamental part of the language of quantum mechanics, linear algebra may be roughly thought of as the study of vectors, and how they transform. As I shall discuss in a future post, by using the idea of a basis, we can represent a special kind of vector transformation by an object called a matrix (more generally, an operator). Thus, what we have discussed thus far is not a set of disparate islands so much as a set of stepping stones. If you prefer a more concrete metaphor, we have poured a foundation for future discussions, including a discussion of the quantum state itself.

Once we have the idea of a quantum state, the horizon opens wide for exploration. The quantum state gives us a language in which we can understand seemingly arcane consequences of a world described by quantum mechanics, such as entanglement or superposition. With the formal tools of mathematics at our disposal, we can overcome the limitations of our intuition, so that we can understand even such tricky concepts as these.

One downside to my stepping-stone approach, however, is to seemingly put the concept of a quantum state on a pedestal, inaccessible without a high degree of mathematical maturity. Little could be further from the case. Indeed, the mathematics with which we understand quantum states are not so difficult as they are esoteric. It is my own opinion that these areas of math need not be esoteric, save for that it has been arbitrarily decided upon (at least in my home, the United States) that Math Is Hard, and that concepts such as those discussed here Should Be Left To the Professionals. Bollocks. We live in a probabilistic world, and one in which statistics guide nearly every aspect of society, so why should understanding probability be so inaccessible? While complex numbers are not so manifestly real, even to the point that i is called the imaginary unit, it takes but a small amount of study to see that the complex numbers form an integral part of how we describe reality. Similarly, the concept of a vector may seem too far removed from reality for the layman to pursue, but in many ways, vectors formalize and encode much of our intuition about geometry, and are just as accessible as the sort of geometry that is taught in many grade schools.

No, quantum states are there for those who want them. My goal is to bring the concepts just a little bit closer, and to let the mathematical beauty underlying them shine through just a little bit brighter. In doing so, I won't always go from point to point in most straightforward way, but I ask your patience, for I am going somewhere. With a bit of looking back at what is, I hope you'll agree that we're going somewhere interesting.

The Power of Conversation

Today, I had a conversation with a friend of mine. One of those wonderful, roaming conversations that managed to touch both on the merits of various tabletop roleplaying game systems and on the utility of deriving quantum mechanics from quantum field theory. You know, the kinds of conversations that you can have with awesome people. Along the way, we spent a while discussing a topic near and dear to my blogging interests: science and rationality in society.

Perhaps unsurprisingly, we agreed on most of what we talked about with respect to this important topic. Looking back has gotten me thinking about the pragmatic value of keeping the rationality conversation alive, even with like-minded people. There are many reasons that often come up in such meta-discussions, of course. Conversing with others can help you to realize that you aren't alone in everything, just as Darwin fish can serve to raise consciousness about the existence of freethinkers. Such conversations can help one to hone their arguments and develop confidence in their conclusions. Through conversation, we can also expose ourselves to novel motivations and arguments, even for positions we may already take. For the emotional reasons alone, it's worthwhile to keep talking about rationality and science, to say nothing of these kinds of pragmatic benefits.

That said, there's one purpose that conversation can serve that I feel deserves special emphasis. Through conversing with other people, whether like-minded or diverse, we can learn quite a bit about when we are wrong. We are all human (I presume, anyway), and are fallible in our applications of logic. As such, it is a wonderful opportunity for self-improvement to be able to hash through our views with those honestly seeking truth. Indeed, just as science is inherently a self-correcting enterprise that must deal with the limitations of human minds, so too must rationality in general co-exist with a self-awareness of our capacity for mistakes. In conversations with others, we are often called upon to defend, explain or otherwise make explicit those private ideas which shape how we understand the world. When we are in the wrong on an issue, this process can be a tremendously helpful mechanism for self-improvement. Even with like-minded people, one's justifications can be flawed in ways discoverable through open and honest debate.

Conversation, then, is an essential tool in the rationalist's toolbox. Without healthy conversation, we are each isolated and limited to the power of our own brains. This is a large part of why I appreciate having a healthy and vibrant discussion take place on articles that I post here, such as that attached to Context Isn't Everything. By the time that you, dear readers, invest in this nascent community, I am given a precious opportunity to discover the depths of my own wrongness, as well as to find points of agreement with my intelligent, rational and compassionate peers. The rationality conversation is everywhere, and I'm glad for what parts of it find their way here, conveyed by vibrant minds.